IPad – How iPad screen gameplay is captured

Number 1 is exactly true, unless the developer chose to output the gameplay through the cable. A few games do this, but most do not.

Number 2 is exactly true.

On your last question, I'm not 100% certain and haven't tried it (I don't have the component cables). Video mirroring from the iPad 2 works with the VGA adapter, so it would likely work with the component cables, but I can't guarantee it.

Edit: Looking at the specs on Apple's site under TV & Video, it seems pretty clear that component out work with the apps that do video out, but not for mirroring.

I'm surprised nobody has answered this correctly.

The solution is to open iTunes, click on your iPhone, go to the Photos tab, then Sync Photos for the folder that contains the photo and video subfolders you want to sync. Each subfolder will then be sync'ed to your iphone UNDERNEATH the Camera Roll as new Albums, and these are treated seperately than the Camera Roll and will always remain synced.

Furthermore, apps that can access the Camera Roll almost always can also access Synced Albums, so this should really work well for you. I keep a whole bunch of old photos and videos on my iPhone at all times using this method and it works great.

As a bonus, unlike the Camera Roll, these Synced Albums don't get backed up in iTunes, so it won't slow down your Backup like a growing Camera Roll will.